Question

Prove that 3 + 4√5 is an irrational number.

Answer 1

Given, To prove - 3+4√5 is an irrational number

So first let's assume 3+4√5 is a rational number

We know all rational numbers are in the form p/q

So,

$3 + 4 \sqrt{5} = \frac{p}{q} \\ \\ 4 \sqrt{5} = \frac{p}{q} - 3 \\ \\ 4 \sqrt{5} = \frac{p - 3q}{q} \\ \\ \sqrt{5} = \frac{p - 3q}{4q}$

( irrational ) ≠ ( rational )

So our assumption is wrong and hence 3+4√5 is irrational number....

Answer 2

Answer:

let us assume that3+4 root 5 is a rational number 3+4root5 = p/q(p.q€z, q not equal to 0 and (p, q) =1)

4root 5=p/q-3

root 5=p-3q/4q

here p-3q/4q is a rational number but root 5is an irrational number this is not possible so our assumptions is wrong therefore 3+4root5 is an irrational number